【作者】 雷雪萍；

【导师】 朱作桐；

【作者基本信息】 南京师范大学 ， 基础数学， 2002， 硕士

【摘要】 W．C．Holland 1963年证明了格序群可表示为某一全序集上的格序置换群[16]，因此格序置换群是研究格序群的重要工具之一。本文首先介绍了可迁性，这个在格序置换群里起重要作用的概念，并利甲格序群的稳定子群，给出了可迁格序置换群是2-可迁的等价条件；讨论了本原分量，且给出了可迁格序置换群是正规值的一些等价条件。 在第三章，我们介绍了格序置换群的凸同余，并研究了可迁格序置换群的凸同余与块所决定的可迁格序置换群的分类；讨论了可迁格序置换群的凸同余和块的性质以及它们之间的关系。更多还原

【Abstract】 W.C.Holland[1963] has proven that every lattice-ordered group is (isomorphic to) a subgroup of the lattice-ordered group of all order-preserving permutations of a chain. So lattice-ordered permutation groups are important tools for describing the structure of lattice-ordered groups. In this paper, what we discuss is on the lattice-ordered permutation groups.In chapter two of this paper, we introduce the transitivity, which is an important definition in the 1-permutation group. And then we give some necessary and sufficient conditions for the transitive 1-permutation groups to be 2-transitive by using the stabilizer subgroups of the transitive 1-permutation groups. We also give some necessary and sufficient conditions for the transitive 1-permutation groups to be normal-valued.In chapter three of this paper, we introduce the convex congruences of 1-permutation groups. Then we research the classifications and the congruences of the transitive 1-permutation group, which is determined by the block. Furthermore, we discuss the property of the congruences and the blocks, and relationships between them.更多还原